Problem: Solve for $x$ and $y$ using elimination. ${-2x-5y = -47}$ ${-5x+4y = 31}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $5$ ${-8x-20y = -188}$ $-25x+20y = 155$ Add the top and bottom equations together. $-33x = -33$ $\dfrac{-33x}{{-33}} = \dfrac{-33}{{-33}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {-2x-5y = -47}\thinspace$ to find $y$ ${-2}{(1)}{ - 5y = -47}$ $-2-5y = -47$ $-2{+2} - 5y = -47{+2}$ $-5y = -45$ $\dfrac{-5y}{{-5}} = \dfrac{-45}{{-5}}$ ${y = 9}$ You can also plug ${x = 1}$ into $\thinspace {-5x+4y = 31}\thinspace$ and get the same answer for $y$ : ${-5}{(1)}{ + 4y = 31}$ ${y = 9}$